What is the probability that when chosen at random, there will be at least 2 different races in this 3 person team?

The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

The proportion should be sufficiently demonstrated to be lower than 49% at the 0.05 level.

Given,

Less than 49% of a newsletter publisher's subscribers, in their estimation, own a personal computer.

A potential advertiser wants to verify this claim for marketing purposes.

The marketer chooses to reject the null hypothesis after running a test with a 0.05 level of significance.

We have to determine the conclusion regarding the publisher's claim;

Here,

Null and Alternative hypothesis;

H₀ = P ≥ 0.49

H₁ = P < 0.49 (Left tailed test)

The significance level is 0.05

So,

0.05 < 0.49

Then,

At the defined meaning level, it is chosen to reject the null hypothesis.

Therefore,

There should be sufficient evidence that the proportion is lower than 49% at the 0.05 level.

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Answer:

I am pretty sure it’s either the first one or the last one

Step-by-step explanation:

Answer:

maybe its a and e

Step-by-step explanation:

Answer: A and E

Explanation:

A has a triangle to show the slope. If you count the boxes along the triangle the vertical side is 10 boxes and the horizontal side is 4. This means the slope is 10/4 which simplifies to 5/2.

E doesn’t have a triangle to show the slope but if you count in the triangle pattern from one point to the next point the slope equals 5/2.

Answer:

solve it your self

aafai gar

jatha

bujish

The temperature on mountaintop was -10° and the temperature on the ground was 10°. The solution has been obtained by using the linear equation.

What is a linear equation?

One is the degree of the linear equation. It is obvious that there are no variables in linear equations with exponents greater than 1. The graph's equation results in a straight line.

We are given that the temperature on the mountaintop was 20° lower than temperature on the ground.

Let the temperature on the ground be 'x'.

So, temperature on the mountaintop = x - 20

Also, the temperature on a mountaintop and the temperature on the ground had opposite values.

So,

x = - (x - 20)

On solving this, we get

⇒x = -x + 20

⇒2x = 20

⇒x = 10°

So, x - 20 = 10 - 20 = -10°

Hence, the temperature on mountaintop was -10° and the temperature on the ground was 10°.

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The height of the triangular face is 15 yards.

To find the height of the triangular face, we will use the formula for the volume of a triangular prism:
Volume = (1/2) * Base * Height * Length.

We are given the following values:
- Volume (V) = 720 cubic yards
- Length (L) = 8 yards
- Base (B) = 12 yards
We need to find the height of the triangular face (H).

Let's plug in the given values into the formula and solve for H:
720 = (1/2) * 12 * H * 8
First, simplify the equation:
720 = 6 * H * 8
720 = 48 * H
Now, divide both sides by 48 to find the value of H:
H = 720 / 48
H = 15 yards.

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Answer:

Step-by-step explanation:

$31.10

The probability of rolling a number greater than 6 is 1/4, or 0.25 as a decimal, or 25% as a percentage.

The die has 8 equally likely possible outcomes, which are the numbers 1 through 8. The probability of rolling a number greater than 6 is the same as the probability of rolling a 7 or 8.

Since each of these two outcomes is equally likely, the probability of rolling a number greater than 6 is:

P(rolling a number greater than 6) = P(rolling a 7) + P(rolling an 8)

The probability of rolling a 7 is 1/8, and the probability of rolling an 8 is also 1/8. Therefore:

P(rolling a number greater than 6) = 1/8 + 1/8 = 2/8 = 1/4

So the probability of rolling a number greater than 6 is 1/4, or 0.25 as a decimal, or 25% as a percentage.

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Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

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The value of tan(t−π) is 4/9.

According to the statement

we have given that  tan(t)=4/9 and we have to find the value of tan(t−π).

So,

tan(t−π)  -(1)

take negative sign common from equation (1) it then

tan(t−π) = -tan(-t+π)

and we know that the according to the mathematics formula it become

tan(-t+π) is -tan t

then

tan(t−π) = -(-tan t)

it becomes

tan(t−π) = tan t

then its value becomes

tan(t−π) = tan(t)=4/9.

because we have given that the value of tan t is tan(t)=4/9.

So, The value of tan(t−π) is 4/9.

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Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

Answer:

B

Step-by-step explanation:

To rotate triangle ABC about the origin 90° clockwise we would follow the rule (x,y) → (y,-x), where the y-value of the original point becomes the new x-value and the x-value of the original point becomes the new y-value with the opposite sign.

Answer:

0.004

Step-by-step explanation:

The question is tell us 2/5% or 0.4%. We simply divide 0.4 by 100 to get our answer of 0.004.

Gathering together representatives from various organizations that have an interest in a particular policy, defining goals, setting an agenda, and devising strategies for action are all major components of policy formulation and implementation through collaborative processes.

Collaborative policy-making involves bringing together stakeholders from diverse organizations, such as government agencies, non-profit organizations, advocacy groups, and industry representatives, to collectively address complex policy issues. This participatory approach aims to foster cooperation, dialogue, and shared decision-making among stakeholders. The first step involves gathering representatives from these organizations to ensure a comprehensive representation of perspectives and interests. Once assembled, the stakeholders work together to define common goals, set an agenda, and develop strategies for action. This collaborative effort allows for the pooling of knowledge, expertise, and resources, enabling stakeholders to collectively shape policies that are more inclusive, effective, and sustainable. By involving various stakeholders in the policy formulation process, collaborative approaches promote transparency, legitimacy, and buy-in from those who will be affected by the policy. This helps to enhance the quality of decision-making, build consensus, and increase the chances of successful policy implementation.

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Answer:

Yeah 10

Step-by-step explanation:

40 will give her more

The words savage and savory are neither similar nor contradictory.

Contradiction is a term used to indicate mutually opposite things. It is commonly used in statements where both the statements cannot be true.

Savage is a word the meaning of which is wild or non cultivated in a context as an adjective. In another context, savage can be used as a noun to define an uncivilized or a brutal human.

On the other hand, savory is a completely different term which is used to define the taste of the dishes, typically in a positive way.

Hence the terms savage and savory are neither similar nor contradictory words.

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Answer:

1,350

Step-by-step explanation:

15% of 9,000 is 1,350, you can multiply 9000 by .15.

Answer:

The corresponding angles are congruent but not supplementary angles because the Supplementary may have any two other angles which their sum is 180 show the corresponding angles are congruent if you understand please like and follow me.

Answer: x=22

Step-by-step explanation:

Since the angles are corresponding angles, use x+14=5x-74. You get 36=36 meaning it is right when you substitute the value for x.

x+14=5x-74

-x on both sides

14=4x-74

+74 on both sides

88=4x

Divide both sides by 4

x=22

Answer:

20% off means that the new price of the skirt will be 80% of the original price:

$30(100%  – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100%  – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

Step-by-step explanation:

20% off means that the new price of the skirt will be 80% of the original price:

$30(100%  – 20%) = $30(80%)

Converting the percent to a decimal gives:

$30(0.8) = $24.00

There is an additional 15% off the sale price of $24.00, so the final price is 85% of the sale price:

$24(100%  – 15%) = $24(85%)

Again converting the percent to a decimal gives:

$24(0.85) = $20.40

Answer:

50 Fahrenheit (F) 10 Celsius (C)

1 F = -17.222 C 1 C = 33.800 F

Answer:

50 Fahrenheit (F) 10 Celsius (C)

1 F = -17.222 C 1 C = 33.800 F

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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The required answer is  the antiderivative of s(x) is: 4x^2 + 4x

Given that s(x) = -1x + 8 + 9x - 4, we want to find the antiderivative of s(x) without including the constant C.
Antiderivatives are also called general integrals, and sometimes integrals. The latter term is generic, and refers not only to indefinite integrals but also to definite integrals. If the word integral is used without additional specification, the reader is supposed to deduce from the context whether it refers to a definite or indefinite integral. Define the indefinite integral of a function as the set of its infinitely many possible antiderivatives.
First, simplify s(x):
s(x) = -1x + 9x + 8 - 4
s(x) = 8x + 4
A antiderivative is a function reverses, they are taken the form of a function is an arbitrary constant. By second fundamental theorem of calculus , the antiderivative is related to the definite integral . Definite integral of a new function over a band interval.
Now, find the antiderivative of s(x):
Antiderivative of 8x + 4 = (8/2)x^2 + 4x
The natural logarithm function, if a positive real variable. This is a  inverse function. Logarithm is useful for solving equations. Decayed constant or unknown time in problems.  
So, the antiderivative of s(x) is:
4x^2 + 4x

where the function is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.

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The mode best represents the set of data: red, blue, red, yellow, red, green, black, red, white, red. The mode is a statistical measure that represents the most frequently occurring value or values in a dataset.

The mode is the measure of center that represents the most frequently occurring value in a dataset. In this case, the color "red" appears most frequently, occurring 6 times out of the 11 data points. Therefore, the mode of the dataset is "red."

The mean, on the other hand, calculates the average value by summing all the data points and dividing by the total number of data points. The mean can be influenced by extreme values or outliers, which may not accurately represent the overall data.

The median is the middle value when the data is arranged in ascending or descending order. In this case, since there are 11 data points, the median would be the sixth value. However, there is no clear middle value as there are multiple occurrences of "red" in the dataset.

Hence, the mode, representing the most frequently occurring value, is the measure of center that best represents this set of data.

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John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.

To determine how many images John must scan before his total cost is less than getting scanned images at the computer center, we can set up an equation.

Let's denote the number of images John needs to scan as "x."

The total cost for John to scan x images is given by:

John's total cost = cost of scanner + cost of supplies + cost per image scanned

John's total cost = $215.70 + ($0.34 * x)

The total cost for scanning x images at the computer center is given by:

Computer center's cost = cost per image scanned * x

Computer center's cost = $0.59 * x

We want to find the point at which John's total cost is less than the computer center's cost. In other words, we want to find the value of x for which John's total cost is less than the computer center's cost:

John's total cost < Computer center's cost

$215.70 + ($0.34 * x) < $0.59 * x

Now, we can solve for x:

$215.70 + ($0.34 * x) < $0.59 * x

$215.70 < $0.59 * x - $0.34 * x

$215.70 < $0.25 * x

Divide both sides of the inequality by $0.25:

$\frac{215.70}{0.25} < \frac{0.25 * x}{0.25}$

862.80 < x

Therefore, John must scan more than 862 images before his total cost is less than getting scanned images at the computer center.

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9 square yards..........

Answer:

-9/6

Step-by-step explanation:

Answer:

-3/2    -1/2     -1.5

good luck!!!!

Answer:

It will make 4 90° turns, because each 1/4 turn or 15 minutes is 90°.

Answer:

Gavin has 3 parts left.

Step-by-step explanation:

8-3-2=3. The time was not important.